For calculating the branching ratio of the \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_J)\eta \)  transitions, the concrete phenomenological model should be involved. Borrowing the former experience of the decays of higher states of heavy quarkonium, the coupled channel effect should be considered here [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}. In this work, we adopt the hadronic loop mechanism to present the concrete calculation, which will be mentioned in the following section.
We hope that our realistic investigation of the discussed processes may provide valuable information to experimentally search for \(\Upsilon (10753)\rightarrow \Upsilon (1^3D_J)\eta \) , which will be an intriguing research task for Belle II.
